(390625)/(125 t)-(2 t^2)/(125 t)-(625 t)/(125 t) geq 0

Question

Answer 1

To solve the inequality

, we can simplify each term by factoring out the common denominator of

:

Combine the terms over the common denominator:

Now, we need to solve the inequality

. To do this, we can multiply both sides of the inequality by

(assuming

):

Rearrange the terms:

Now, we need to solve the quadratic inequality

. We can use the quadratic formula to find the roots of the corresponding quadratic equation

:

Here,

,

, and

. Plugging in these values, we get:

So, the roots are:

Since the coefficient of

is positive, the parabola opens upwards, and the solution to the inequality

is the interval between the roots:

However, since

must be positive (as it is in the denominator), the final solution is:

So, the solution to the inequality

is

.

Вопрос